Colloquium

On the Convexity of Neural Codes

11/04/2015 - 4:15pm
11/04/2015 - 5:15pm
Speaker: 
Bill Kronholm (Whittier College)
Abstract: 

Neurons transmit electrical signals through the nervous system, and the patterns of firing neurons invoke responses from the host. For certain neurons, it is reasonable to assume that the receptive field for the neuron (the region in the stimulus space within which that neuron fires) is a convex region in some Euclidean space. In this talk, we discuss ways to detect whether or not a particular collection of neural firing patterns can arise from convex receptive fields. 

 

Where: 
Argue Auditorium, Millikan, Pomona College

TOPOLOGICAL SYMMETRY GROUPS

10/28/2015 - 4:15pm
10/28/2015 - 5:15pm
Speaker: 
Erica Flapan (Pomona College)
Abstract: 

Chemists have defined the point group of a molecule as the group of rigid symmetries of its molecular graph in R3. While this group is useful for analyzing the symmetries of rigid molecules, it does not include all of the symmetries of molecules which are flexible or can rotate around one or more bonds. To study the symmetries of such molecules, we define the topological symmetry group of a graph embedded in R3 to be the subgroup of the auto- morphism group of the abstract graph that is induced by homeomorphisms of R3. This group gives us a way to understand not only the symmetries of non-rigid molecular graphs, but the symmetries of any graph embedded in R3. The study of such symmetries is a natural extension of the study of symmetries of knots. In this talk we will present a survey of results about the topological symmetry group and how it can play a role in analyzing the symmetries of non-rigid molecules.

 

Where: 
Argue Auditorium, Millikan, Pomona College

Post Colloquium, Non-Colloquium Party

09/02/2015 - 4:15pm
09/02/2015 - 5:15pm
Speaker: 
N/A
Abstract: 

The traditional year-opening social event for the Claremont Colleges Mathematics Community, will be held at the Sky Cube, in the Shanahan Center for Teaching and Learning, HMC. Spouses, partners, and family are welcome. Professor Deanna Needell (CMC) and Professor Mohamed Omar (Harvey Mudd), Colloquium co-chairs, hope to see everyone there for refreshments, and other pleasant pursuits.

Where: 
Sky Cube, Shanahan Center for Teaching and Learning, Harvey Mudd College, 320 E. Foothill Blvd

Mathematical Methods in Data Science

01/27/2016 - 4:15pm
Speaker: 
Andrea Bertozzi (UCLA)
Abstract: 

 

This talk is about current research in algorithms for "big data".  We will focus on two classes of models - (1) topic modeling for document classification (2) algorithms based on graphical models used for hard clustering of big data. Many of these methods can be understood with a basic undergraduate math background including linear algebra.  For topic modeling we will discuss basic models like nonnegative matrix factorication and latent dirichlet allocation.  For the graphical methods we introduce the graph Laplacian and present spectral clustering methods and also some recent graph-cut based methods developed at UCLA. Examples of data are diverse from hyperspectral imagery to twitter data 

 

Where: 
Argue Auditorium, Millikan, Pomona College

Knots, Surfaces, 3-manifolds, and the Kakimizu Complex

12/09/2015 - 4:15pm
12/09/2015 - 5:15pm
Speaker: 
Robin Wilson (Cal Poly Pomona)
Abstract: 

The study of knots, surfaces, and 3-manifolds is part of a subfield of mathematics known as low-dimensional topology that involves the study of topological spaces of dimensions one through four.  The areas of knot theory and 3-manifold topology are closely related.  In fact, the exterior of a knot is itself an example of a 3-manifold.  One approach to studying 3-manifolds is to understand the surfaces that are contained in them.  In this talk I will give an introduction to knot theory, its connections with 3-manifold topology, and the study of surfaces in 3-manifolds and knot exteriors.  I will also discuss some recent research about Seifert surfaces in knot complements.  The talk is intended to be accessible to students of mathematics at all levels.

Where: 
Argue Auditorium, Millikan, Pomona College

Some people have all the luck... or do they?

12/02/2015 - 4:15pm
12/02/2015 - 5:15pm
Speaker: 
Skip Garibaldi (CCR)
Abstract: 

Has anyone you know ever won a prize worth $600 or more in the lottery? It's a rare thing for someone to win even just one. But when we investigated records of all claimed lottery prizes in Florida, we discovered that some people had won hundreds! Winning so much is not just lucky, but suspiciously lucky. I will explain what we thought they might have been up to, what mathematics says about it, what further investigations revealed, and the law enforcement actions and state policy changes that occured as a consequence of our theorems. 

This talk is joint work with Richard Arritira, Lawrence Mower, and Philip B. Stark. 

Where: 
Argue Auditorium, Millikan, Pomona College

Factoring Unfactorable Polynomials

11/18/2015 - 4:15pm
11/18/2015 - 5:15pm
Speaker: 
David Eisenbud (UC Berkeley)
Abstract: 

Everyone learns in elementary algebra to factor the polynomial x^2-y^2 as (x+y)(x-y), but one must enlarge the real numbers to the complex numbers in order to factor x^2+y^2. However, x^2-y^3 can’t be factored as a product of polynomials, even over the complex numbers. I’ll explain a fruitful way of enlarging the universe of discourse to include factorizations of such unfactorable polynomials, and some of its applications. The area is rich with open problems that are easily understood.

Where: 
Argue Auditorium, Millikan, Pomona College

Some faces of Compressed Sensing in applications

11/11/2015 - 4:15pm
11/11/2015 - 5:15pm
Speaker: 
Tobias Bimbaum (TU Bergakademie Freiberg)
Abstract: 

Compressed Sensing (CS) is a new signal processing theory which can give a

substantial performance boost to various inverse problems. With now roughly 11
years after the first fundamental contributions from Candés, Romberg and Tao,
the basic theory is well understood. Since CS is so widely applicable an
enormous variety of applications has been considered in recent years.

This talk is going to give a short primer on the basic CS theory, thereby
pointing out its basic ideas, and introduce some less investigated applications

 

Where: 
Argue Auditorium, Millikan, Pomona College

Nonstandard Methods in Combinatorics

10/21/2015 - 4:15pm
10/21/2015 - 5:15pm
Speaker: 
Martino Lupini (Cal. Tech.)
Abstract: 

I will give an introduction to nonstandard analysis, and then present an overview of the application of nonstandard methods to problems in combinatorics of numbers.

Where: 
Argue Auditorium, Millikan, Pomona College

Linear Algebra as a Natural Language for Special Relativity and Its Paradoxes.

10/14/2015 - 4:15pm
Speaker: 
John de Pillis (UC Riverside)
Abstract: 

See Attachment

Where: 
Argue Auditorium, Millikan, Pomona College
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